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Stabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations. (English) Zbl 1129.35004
A stabilized finite element method with the Crank-Nicolson extrapolation in time is studied theoretically. The method is applied to the incompressible Navier-Stokes equations and the error analysis is presented. For the finite element approximation the Q1-P0 quadrilateral element or the P1-P0 triangle element are used. The viscous and pressure terms are approximated implicitly in time. The nonlinear convection term is approximated semi-implicitly. The authors show, for example, that the L (0,T;L 2 (Ω)) error is of order O(h 2 +τ 3/2 )·
MSC:
35A35Theoretical approximation to solutions of PDE
35Q30Stokes and Navier-Stokes equations
65N15Error bounds (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
76D06Statistical solutions of Navier-Stokes and related equations